Re: [Phys-L] the sign of g

[Philip Keller <pkeller@holmdelschools.org>]

This is no doubt an issue that many beginners struggle with.  I do teach my
students that the sign on their free-fall acceleration term depends on
their chosen coordinate system.  But for many of them, you have to be more
specific.  They often choose the coordinate system without realizing that
they have chosen!  So it is not really just the sign of g that is the
problem.

When a problem says "A ball that is launched upward from the ground at 30
m/s.  Find its displacement and velocity 5 seconds later" and they write:
"V-initlal = 30 m/s", you have to show them that they just chose a
coordinate system.  The sign of g is just one issue they face.  The also
have to know how to interpret the signs of the other quantities that they
may solve for.   BTW I agree with the suggestion of showing the solution
using V-initial = -30 m/s.

Same applies when "a ball is dropped from a 100-m cliff."  You can
certainly write "d=100 m" but you should be aware that you just made a
decision about the coordinate system. Again, showing the solution with
d=-100 m also helps.  But make explicit the moment when the coordinate
system is chosen.

Still, a thorny issue for beginners...

On Mon, May 9, 2016 at 1:21 PM, Richard Tarara <rtarara@saintmarys.edu>
wrote:

> There are many ways to tackle this problem and others have presented
> some.  I would only emphasize that breaking the idea that 'g' carries an
> intrinsic negative sign will help later on when you have to be careful
> about forces between charges where students want to carry the signs into
> the algebra.  Again it is a case of setting a coordinate system and using
> attractive/repulsive to determine the direction (and therefore the sign) of
> the force on a given charge.
>
> rwt
>
> On 5/9/2016 11:28 AM, stefan jeglinski wrote:
>
> > This slays large populations of students on that first exam, and seems to
> > be a serious mental block for them: whether g = +9.8 or -9.8 (units
> > suppressed, substitute the English version over metric if you like). I
> > teach that the sign can't be determined unless a coordinate system is
> > defined, which is a separate but critical step in setting up any problem,
> > but they like to rush. Many will inadvertently (or with intent) define a
> > coordinate system (e.g., up is positive), which naturally works the signs
> > into the algebra, but then at the end, will say "well g is always -9.8" and
> > introduce a sign error when they get out their calculators.
> >
> > I've taken to teaching that g=+9.8 or g=-9.8 is the incorrect way to
> > think about it. Rather, g has merely a value of 9.8, and the sign is an
> > "artificiality" that has nothing to do with g per se. The pushback I get is
> > that "9.8 is the same as +9.8" and I push back in return on that but to
> > skeptical looks.
> >
> > My question is: is there a good mathematical argument I can cite (aside
> > from a coordinate system) for why +9.8 and 9.8 are not the same thing? Or
> > am I myself wrong?
> >
> >
> > Stefan Jeglinski
> >
> >
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>
> --
> Richard Tarara
> Professor Emeritus
> Saint Mary's College
>
> free Physics educational software
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